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There have been several studies suggesting that protein structures solved byNMR spectroscopy and x-ray crystallography show significant differences. Tounderstand the origin of these differences, we assembled a database ofhigh-quality protein structures solved by both methods. We also findsignificant differences between NMR and crystal structures---in theroot-mean-square deviations of the C$_{\alpha}$ atomic positions, identities ofcore amino acids, backbone and sidechain dihedral angles, and packing fractionof core residues. In contrast to prior studies, we identify the physical basisfor these differences by modelling protein cores as jammed packings ofamino-acid-shaped particles. We find that we can tune the jammed packingfraction by varying the degree of thermalization used to generate the packings.For an athermal protocol, we find that the average jammed packing fraction isidentical to that observed in the cores of protein structures solved by x-raycrystallography. In contrast, highly thermalized packing-generation protocolsyield jammed packing fractions that are even higher than those observed in NMRstructures. These results indicate that thermalized systems can pack moredensely than athermal systems, which suggests a physical basis for thestructural differences between protein structures solved by NMR and x-raycrystallography.

Analyses of protein cores reveal fundamental differences between solution and crystal structures